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COMEDK · Maths · 8. Trigonometric Ratios & Identities

The expression \(\dfrac{2 \tan A}{1-\cot A}+\dfrac{2 \cot A}{1-\tan A}\) can be written as

  1. A \(\sec 2 A+\operatorname{cosec} 2 A\)
  2. B \(\sin 2 A+\cos 2 A\)
  3. C \(\tan 2 A+\cot 2 A\)
  4. D \(2 \sec A \operatorname{cosec} A+2\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(2 \sec A \operatorname{cosec} A+2\)

Step-by-step Solution

Detailed explanation

\(\dfrac{2\tan A}{1 - \cot A} + \dfrac{2\cot A}{1 - \tan A}\) \(= 2\left[\dfrac{\frac{\sin A}{\cos A}}{\frac{\sin A - \cos A}{\sin A}} + \dfrac{\frac{\cos A}{\sin A}}{\frac{\cos A - \sin A}{\cos A}}\right]\)…